(a) Field of the Invention
This invention relates to a method for waveform analysis, and more particularly, to an improved method for non-harmonic analysis of waveforms in which intervals and/or frequencies (or periods) for analysis can be selected in an arbitrary manner. More particularly, the invention concerns such method which finds utility in a wide variety of applications that require waveform processing, such as interpolation of a waveform with missing portions, restoration of a clipped (or saturated) waveform, waveform prediction, processing of image and sound signals, determination of the pitch period of a harmonic waveform and the like.
(b) Description of the Prior Art
Heretofore, various methods for waveform analysis have been proposed for purposes of waveform synthesis, noise suppression, bandwidth compression and the like. Those previous methods are exemplified by Applicant""s PCT Application No. PCT/JP94/00146 which was published on Aug. 18, 1994 under International Publication No. WO 94/18573. As is well known, the Fourier analysis is typical of the harmonic analysis to be applied to one continuous section of a waveform, and the Fourier transform such as DFT and FFT is represented by a number of sinusoids having a harmonic relationship. Accordingly, the waveform resulting from the inverse Fourier transform is a repetition of the particular internal of the original waveform and does not provide any information for other sections of the waveform. The general harmonic analysis known as Prony""s method provides for detection of sinusoids which actually constitute a waveform to be analyzed and, in principle, permits a restoration and prediction of the waveform through waveform synthesis. However, the method has not been put into practical use because the number of sinusoids constituting the waveform must be known and also because the method is susceptible to influences by noises.
It is a general object of the invention to provide an improved method for non-harmonic waveform analysis which permits freedom of selecting intervals and/or frequencies (or periods) for analysis.
It is another object of the invention to provide an improved method for non-harmonic waveform analysis that is less susceptible to influences by noises than the prior art.
It is a further object of the invention to provide an improved method for non-harmonic waveform analysis which can be used for interpolation, extrapolation or prediction of waveforms.
Accordingly, the invention is generally directed to a method for making a non-harmonic frequency analysis of a discrete waveform, comprising: multiplying an arbitrary interval of a discrete waveform to be analyzed by a sine function having an arbitrary period to provide a first product value; summing the first product value over the arbitrary interval to provide a first summation value; multiplying the arbitrary interval of the discrete waveform by a cosine function having the arbitrary period to provide a second product value; summing the second product value over the arbitrary interval to provide a second summation value; multiplying the sine function and the cosine function to provide a third product value;
summing the third product value over the arbitrary interval to provide a third summation value; squaring the sine function to provide a fourth square value; summing the fourth square value over the arbitrary interval to provide a fourth summation value; squaring the cosine function to provide a fifth square value; summing the fifth square value over the arbitrary interval to provide a fifth summation value; and deriving a plurality of sinusoids contained in the discrete waveform based on the first to fifth summation values.